Micas like muscovite and biotite break along flat planes because

Biotite and muscovite cleave as they do as a result of their molecular structure and the bonds between layers of the mineral. Muscovite for example, being a mica mineral, is composed of tightly bonded silica, aluminum and hydroxide ions within each layer and held together by weaker potassium ions. Thus, when breaking pressure is applied to the mica, it is much more likely that the molecular bonding will break along the weaker potassium bonds than internally. This reaction was so predictable that the name muscovite came from the fact that the mineral could be split so thinly that is was used for a glass substitute in Russia.